TWO VERTICES OF AN ISOSCELES TRIANGLE IS (2,0) AND (2,5).FIND IT’S THIRD VERTEX.. NO SPAMMING SPAMMING MAY LEAD TO DELETION OF UR ACCOUNT..

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TWO VERTICES OF AN ISOSCELES TRIANGLE IS (2,0) AND (2,5).FIND IT’S THIRD VERTEX.. NO SPAMMING SPAMMING MAY LEAD TO DELETION OF UR ACCOUNT.. THANK YOU!!

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1 month 2021-10-27T02:44:49+00:00 2 Answers 0 views 0

1. Step-by-step explanation:

hola sis here is ur ans

Let ΔABC be the isosceles triangle, the third vertex be C(a,b).

and A(2,0) and B(2,5)

Let AC and BC be equal sides of the triangle

By distance formula we have,answr

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11th

Maths

Straight Lines

Introduction

Two vertices of an isoscele…

MATHS

Two vertices of an isosceles triangle are (2,0) and (2,5). Find the third vertex if the length of the equal sides is 3.

MEDIUM

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Let ΔABC be the isosceles triangle, the third vertex be C(a,b).

and A(2,0) and B(2,5)

Let AC and BC be equal sides of the triangle

By distance formula we have,

D=

(x

2

−x

1

)+(y

2

−y

1

)

∴AB=

(2−2)

2

+(5−0)

2

=

25

=5

Now,

AC=3 [length of equal sides=3 ]

AC

2

=3

2

=9……….(a)

but by distance formula,

AC

2

=

(a−2)

2

+b

2

………..(b)

Combining (a) and (b)

⇒(a−2)

2

+b

2

=9

⇒a

2

+4−4a+b

2

=9

⇒a

2

+b

2

−4a=5 ———- (1)

Consider BC

BC

2

=

(a−2)

2

+(b−5)

2

but BC=3

∴(a−2)

2

+(b−5)

2

=9

⇒a

2

+4−4a+b

2

+25−10b=9

⇒a

2

+b

2

−4a−10b+20=0 ——- (2)

⇒−10b+20+5=0 ———(from 1 )

⇒10b=25

⇒b=

10

25

=

2

5

Now, a

2

+

4

25

−4a=5

⇒a

2

−4a=

4

−5

⇒a

2

−4a+

4

5

=0

⇒a=

2

16−4∗1∗

4

5

=

2

11

=

2

2+

11

,

2

2−

11

∴ Coordinate of third vertex (a,b) = (

2

2+

11

,

2

5

) and (

2

2−

11

,

2

5

)